Measurement invariance across items is key to the validity of instruments like a survey questionnaire or an educational test. Differential item functioning (DIF) analysis is typically conducted to assess measurement invariance at the item level. Traditional DIF analysis methods require knowing the comparison groups (reference and focal groups) and anchor items (a subset of DIF-free items). Such prior knowledge may not always be available, and psychometric methods have been proposed for DIF analysis when one piece of information is unknown. More specifically, when the comparison groups are unknown while anchor items are known, latent DIF analysis methods have been proposed that estimate the unknown groups by latent classes. When anchor items are unknown while comparison groups are known, methods have also been proposed, typically under a sparsity assumption - the number of DIF items is not too large. However, there does not exist a method for DIF analysis when both pieces of information are unknown. This paper fills the gap. In the proposed method, we model the unknown groups by latent classes and introduce item-specific DIF parameters to capture the DIF effects. Assuming the number of DIF items is relatively small, an $L_1$-regularised estimator is proposed to simultaneously identify the latent classes and the DIF items. A computationally efficient Expectation-Maximisation (EM) algorithm is developed to solve the non-smooth optimisation problem for the regularised estimator. The performance of the proposed method is evaluated by simulation studies and an application to item response data from a real-world educational test

翻译：测量项目间的测量等值是确保调查问卷或教育测试等工具有效性的关键。差异项目功能（DIF）分析通常用于评估项目层面的测量等值性。传统的DIF分析方法需要预先知道比较组（参考组和焦点组）以及锚定项目（一组无DIF的项目）。这类先验信息并非总是可得，因此心理测量学界已提出针对部分信息未知情况下的DIF分析方法。具体而言，当比较组未知而锚定项目已知时，学界提出了潜在DIF分析方法，通过潜在类别估计未知组；当锚定项目未知而比较组已知时，通常在稀疏性假设（DIF项目数量不过多）下也提出了相应方法。然而，当两类信息均未知时，目前尚无DIF分析方法。本文填补了这一空白。在提出的方法中，我们通过潜在类别对未知组进行建模，并引入项目特异性DIF参数来捕捉DIF效应。假设DIF项目数量相对较少，我们提出了一种基于$L_1$正则化的估计器，以同时识别潜在类别和DIF项目。为解决正则化估计器中的非光滑优化问题，开发了一种计算高效的期望最大化（EM）算法。通过模拟研究和实际教育测试项目反应数据应用评估了所提方法的性能。